Flat band in disorder-driven non-Hermitian Weyl semimetals

Abstract

We study the interplay of disorder and bandstructure topology in a Weyl semimetal with a tilted conical spectrum around the Weyl points. The spectrum of particles is given by the eigenvalues of a non-Hermitian matrix, which contains contributions from a Weyl Hamiltonian and complex selfenergy due to electron elastic scattering on disorder. We find that the tilt-induced matrix structure of the self-energy gives rise to either a flat band or a nodal line segment at the interface of the electron and hole pockets in the bulk bandstructure of type-II Weyl semimetals depending on the Weyl cone inclination. For the tilt in a single direction in momentum space, each Weyl point expands into a flat band lying on the plane, which is transverse to the direction of the tilt. The spectrum of the flat band is fully imaginary and is separated from the in-plane dispersive part of the spectrum by the "exceptional nodal ring" where the matrix of the Green function in momentum-frequency space is defective. The tilt in two directions might shrink a flat band into a nodal line segment with "exceptional edge points". We discuss the connection to the non-Hermitian topological theory.

PT -symmetric non-Hermitian Dirac semimetals

“…with H Weyl-ring = sin k x σ 1 + sin k y σ 2 + (M − cos k x − cos k y − cos k z )σ 3 + iλσ i . Actually, H Weyl-ring is a Hamiltonian describing Weyl exceptional rings, which have been theoretically studied [36,37] and experimentally realized [53]. The two Weyl exceptional rings in H kin (k) can be directly distinguished by their imaginary energies.…”

Perspective on topological states of non-Hermitian lattices

“…The interest in non-Hermitian Hamiltonians was originally focused in  -symmetric Hamiltonians [23] as a generalization of quantum mechanics where the Hermiticity constraint could be removed while keeping a real spectra. Today, this has shifted to non-Hermitian Hamiltonians regarded as an effective description of, for example, open quantum systems [24,25], where the finite lifetime introduced by electronelectron or electron-phonon interactions [26][27][28], or disorder [29], is modeled through a non-Hermitian term, or in the physics of lasing [30][31][32][33][34]. An additional source of momentum in this field comes from the study of systems where the quantum mechanical description is used after mapping to a Schrödinger-like equation, as in systems with gain and loss (as found in optics and photonics [35][36][37][38]), surface Maxwell waves [39], and topoelectrical circuits [40,41].…”

Non-Hermitian Exceptional Landau Quantization in Electric Circuits

“…Theoretical efforts were largely ignited by the recognition of the PT -symmetry [2,3], its realization in optics [4][5][6], and further generalizations [7,8]. In physical systems non-Hermiticity can arise directly through incorporating loss or gain but also by viewing Hermitian systems from new angles, including vortex pinning in superconductors [9], topological surface state [10,11], and quasiparticles with self-energy correction [12][13][14][15]. Important developments have recently been focused on the classification of new phases [16][17][18][19][20][21][22], the anomalous bulk-boundary correspondence and skin effect [23][24][25][26][27][28][29][30][31][32], and the bulk Fermi arc and line structures [12,15,33,34].…”